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Mathematics > Combinatorics

Title:
Motzkin Numbers: an Operational Point of View

Abstract: The Motzkin numbers can be derived as coefficients of hybrid polynomials.
Such an identification allows the derivation of new identities for this family
of numbers and offers a tool to investigate previously unnoticed links with the
theory of special functions and with the relevant treatment in terms of
operational means. The use of umbral methods opens new directions for further
developments and generalizations, which leads, e.g., to the identification of
new Motzkin associated forms.